The Resolved Elliptic Genus and the D1-D5 CFT

[2603.18138] The Resolved Elliptic Genus and the D1-D5 CFT Skip to main content Search Submit Donate Log in High Energy Physics - Theory arXiv:2603.18138 (hep-th) [Submitted on 18 Mar 2026 ( v1 ), last revised 25 Aug 2026 (this version, v3)] Title: The Resolved Elliptic Genus and the D1-D5 CFT Authors: Marcel R. R. Hughes , Masaki Shigemori View PDF HTML (experimental) Abstract: This paper is a follow-up to the short paper arXiv:2509.19425 , greatly expanding the discussion with examples and providing derivations and justifications of results presented there. We introduce a new supersymmetry index for the D1-D5 CFT on $T^4$, which we call the resolved elliptic genus (REG). It is a one-parameter generalisation of the standard supersymmetry index, the modified elliptic genus (MEG), and arises naturally in the free symmetric orbifold description of the theory within a new formalism, based on Schur-Weyl duality, that we develop. In this formalism, the Hilbert space of the symmetric orbifold CFT is decomposed into symmetry sectors in which the structure of the states contributing to the MEG is transparent. By examining the action of the supercharge deformed by an exactly marginal operator on the relevant symmetry algebra, we propose a superselection rule governing the lifting process of BPS states, and use it to construct the REG by summing only over those symmetry sectors that can mix according to this rule. The REG exhibits detailed agreement between the CFT and supergravity below the black-hole threshold, a regime in which the MEG is essentially trivial. Above the threshold, the REG is dominated by black-hole microstates, which are now distributed amongst distinct sectors that are invisible to the MEG. We expect both the new formalism and the REG to provide useful new tools for studying the structure of black-hole microstates. In particular, we comment on their possible relevance to the fortuity program for understanding black-hole microstates within CFT. Comments: 45 pages + appendices. V2: References added and minor typos corrected; V3: Typos corrected, matches published version Subjects: High Energy Physics - Theory (hep-th) Report number: YITP-26-27 Cite as: arXiv:2603.18138 [hep-th] (or arXiv:2603.18138v3 [hep-th] for this version) https://doi.org/10.48550/arXiv.2603.18138 Focus to learn more arXiv-issued DOI via DataCite Journal reference: JHEP 07 (2026) 224 Related DOI : https://doi.org/10.1007/JHEP07%282026%29224 Focus to learn more DOI(s) linking to related resources Submission history From: Marcel Hughes [ view email ] [v1] Wed, 18 Mar 2026 18:00:00 UTC (298 KB) [v2] Tue, 14 Apr 2026 01:49:26 UTC (298 KB) [v3] Tue, 25 Aug 2026 03:29:32 UTC (298 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: hep-th < prev | next > new | recent | 2026-03 References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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